Upscaling and Inverse Modeling of Groundwater Flow and Mass ...

176 CHAPTER 7. CONCLUSIONS
travels can further improve the results, and (3) the advection-dispersion equation
can be used at the coarser scale to model the plume migration if careful
modeling/upscaling is performed, as long as the block size remains smaller
than the correlation ranges of the underlying fine scale conductivities.
Chapter 3 presented a three-dimensional transport upscaling methodology
in highly heterogeneous media. This approach introduced an advanced
Laplacian-with-skin hydraulic conductivity upscaling prior to the transport
upscaling. Transport upscaling requires the introduction, at the coarse scale,
of a multi-rate mass transfer process on the classical advection-dispersion equation
for the modeling. The methodology is demonstrated on a 3D synthetic
example. The advantages of the Laplacian-with-skin over other approaches as
well as the multi-rate mass transfer model-based upscaling over the advectiononly-based
upscaling are proved in the exercise.
Chapter 4 introduced a new methodology to model transient groundwater
flow in a high-resolution numerical model by coupling upscaling with ensemble
Kalman filtering. This approach consists of three steps: (1) conductivity
realizations are generated at the scale of the measurements, (2) an advanced
upscaling approach such as the Laplacian-with-skin method is used to reduce
the dimensions of the numerical model, and (3) the ensemble Kalman filter
is used in a set of upscaled conductivity tensors to condition on the observed
piezometric head data. The proposed new method is demonstrated in a 2D
synthetic data-worth exercise.
Chapter 5 applied the ensemble Kalman filter to jointly map hydraulic conductivities
and porosities by assimilating the dynamic piezometric head and
multiple concentration data. Compared with other inverse methods, the EnKF
is remarkable for its computational efficiency, but more importantly for the
easiness to account for multiple types of conditioning data. The capability of
the EnKF for the characterization of conductivities and porosities is demonstrated
in a 2D synthetic example. The uncertainty on flow and transport
predictions is reduced to the minimum when all the data are assimilated.
Finally, in Chapter 6, the normal-score Ensemble Kalman Filter, an algorithm
recently developed to deal with the non-Gaussianity of parameter
and state vectors in EnKF, is used to assess the impact of prior conceptual
model uncertainty on the characterization of conductivity and on the prediction
of flow in a synthetic bimodal aquifer. In addition, the effect of distancedependent
localization functions and different set-ups of the boundary conditions
in the aquifer are also examined. The results are evaluated in terms of
ensemble means, variances and connectivities of the conditional realizations
of conductivity and also looking at the uncertainty of predicted heads after
solving the flow equation in the conditional conductivity realizations. For the
cases analyzed it is found that (i) the patterns of simulated conductivity and
flow prediction can be reproduced close to the reference for both the correct